The Impact of Individual Investment Behavior for Retirement Welfare: Evidence from the United States and Germany

The normative benchmark model from section 3 is based on a simultaneous decision
process. Consequently, we use an empirical estimation strategy that is compatible
with such behavior, a tobit model (Tobin, 1958). This model takes into account that
the dependent variable (percent risky 2) is censored at 0 and 1. The underlying
economic interpretation is that individuals having the value of, for example, 0 for the
risky asset share would actually invest negative shares, but are restricted from doing
so.

5.2 Variable Selection and Expected Signs of Coefficients

The selection of variables is based on the input variables of the normative benchmark
model of section 3. The dependent variable is the risky asset share of investments,
“percent risky 2”. Our dependent variable includes the usual risky assets, but also
real estate and with a negative sign debt. Of course, houses are not as liquid as
stocks, but there is some evidence that individuals adjust their house size according
to their individual situation—that is, they consider the possibility of trading in real
estate (see Banks et al., 2007).¹⁵ The final variable percent risky 2 is obtained by
dividing risky assets by net worth, thus considering debt in both the numerator and
denominator implicitly.

As indicated in Table 2, the independent variables are those that are good candidates
to be compatible with the input for the benchmark model. Thus, we included age, age
squared, dummy variables for gender (female vs. male), education (low or high vs.
middle), occupation (retired vs. employed), the ratio of labor income to net worth (as
a proxy for the labor income-to-cash on hand ratio), and, finally, allowing for non-
CRRA behavior, the logs of labor income and net worth.¹⁶

¹⁵ To include the housing (e.g., Cocco, 2005; Yao and Zhang, 2005) or debt (e.g., Davis,
Kubler, and Willen, 2005) decision or both simultaneously (De Jong, Driessen, and Van
Hemert, 2007) into a normative model is possible in general, but it would render our
optimization approach computationally intractable, due to the large number of cases to be
considered (see section 6).

¹⁶ For a CRRA investor, the ratio of labor income to net worth alone is sufficient to
determine the risky asset share.

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